CALGARY, Alberta, June 8 (Reuters) - Baytex Energy Corp has restarted nearly all the heavy crude output it shut last year, encouraged by the months-long rally in oil prices, a source familiar with the matter said on Wednesday.

It is among the first signs of a North American producer restarting wells that were deemed uneconomic during the deepest part of the global crude price slump.

Around 95 percent of the idled Baytex wells have been turned back on, roughly half of them in May and the rest in June, said the source, who declined to be named because he is not authorised to speak to the media.

"We have not drilled any new wells, but old wells that were uneconomic are coming back on now prices are back up," he said.

The medium-sized producer did not immediately respond to a request for comment, but on a May 3 earnings call Chief Executive Officer James Bowzer said if prices held around $45 a barrel he expected to have most production back online by July.

A year ago, Baytex starting shutting 7,500 barrels per day of low-margin and loss-making conventional heavy oil production in the Peace River and Lloydminster regions in western Canada.

Canada's heavy crude producers were among the first to close active wells last year during the steepest rout in crude prices in a generation. Many have slashed costs and ramped up efficiencies to survive a lower-for-longer market.

While only a small portion of Canada's 3.9 million bpd of capacity, the Baytex restart may kindle concerns in the oil market that fresh supply could snuff out the recent price rally if the pace accelerates.

Canadian Natural Resources Ltd, Husky Energy and Gear Energy also shut in around 5,000 bpd between them last year. Those companies did not immediately respond to queries on whether they had restarted production.

U.S. crude hit a 2016 high on Wednesday of $51.34 a barrel.

In the United States, oil drillers added rigs last week for only the second time this year, but there are few other known examples of existing wells being restarted as producers remain cautious about the sustainability of the price recovery.

Nimble U.S. shale producers, particularly those in the Permian where costs are lower and wells are close to refineries, can make money at $50, but many are still bleeding cash.

Unlike oil sands operations, conventional heavy oil production is quick and relatively cheap to shut and restart in response to changing prices. (Reporting by Nia Williams; Editing by David Gregorio)